Why did stalin becom leader after lenin, not trotsky?

In the beginning, as Lenin end grew nearer, there were five potential leaders, Bukharin, Kamenev, Zinoviev, Trotsky and Stalin. It seemed so obvious that there only was one man to take over Lenin's reign - Trotsky. He was Lenin's right hand man, but a close second was Stalin. People saw him as the one who came second, that's all he was; there was no way that he would beat Trotsky in the race for leadership, …

…absolute control over the party, however, Stalin began to purge from party ranks those leaders and their followers whose loyalty he doubted. Thus the purges began. This is where stalin's stability is questioned, and if he was such a popular and good leader why would he need to be doing this? Not to forget he only got to be ruler of Russia, not by being voted, but by eliminating the opposition some way or another.